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The univalence conditions of some integral operators. (English) Zbl 1267.30054

In this article, the author generalizes some integral operators given by V. Pescar [Gen. Math. 14, No. 2, 77–84 (2006; Zbl 1164.30348)]. Then she studies the univalence conditions for the integral operators defined by the formulae (1.15), (1.16) and (1.17). Under certain conditions, she shows that the resulting functions are univalent.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C55 General theory of univalent and multivalent functions of one complex variable
31A10 Integral representations, integral operators, integral equations methods in two dimensions

Citations:

Zbl 1164.30348
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Full Text: DOI

References:

[1] D. Blezu, “On univalence criteria,” General Mathematics, vol. 14, pp. 77-84, 2006. · Zbl 1164.30327
[2] D. Blezu and R. N. Pascu, “Univalence criteria for integral operators,” Glasnik Matemati\vcki, vol. 36(56), no. 2, pp. 241-245, 2001. · Zbl 1005.30018
[3] V. Pescar, “Univalence of certain integral operators,” Acta Universitatis Apulensis, no. 12, pp. 43-48, 2006. · Zbl 1180.30025
[4] V. Pescar, “A new generalization of Ahlfors’s and Becker’s criterion of univalence,” Bulletin of Malaysian Mathematical Society, vol. 19, no. 2, pp. 53-54, 1996. · Zbl 0880.30020
[5] V. Pescar, “Univalence criteria of certain integral operators,” Acta Ciencia Indica, Mathematics, vol. 29, no. 1, pp. 135-138, 2003. · Zbl 1243.30036
[6] S. Ozaki and M. Nunokawa, “The Schwarzian derivative and univalent functions,” Proceedings of the American Mathematical Society, vol. 33, pp. 392-394, 1972. · Zbl 0233.30011 · doi:10.2307/2038067
[7] V. Pescar, “On the univalence of some integral operators,” General Mathematics, vol. 14, no. 2, pp. 77-84, 2006. · Zbl 1164.30348
[8] Z. Nehari, Conformal Mapping, Dover, New York, NY, USA, 1975.
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